Math goals (DLR Fall 10)

Idealistic statement

"The goal of teachers, like that of parents, should be to make our students, like our children, independent of us."

Other information

Research, some of it my own, shows that the retention a year later of much course material "successfully mastered" by students is a great deal more limited than (some) teachers would like to believe.--Draulston 10:16, 17 September 2010 (CDT)

Comments/Implications

If retention of information is limited, then the teaching style should either emphasize the basics to ingrain them, increasing the chances that they will be remembered (this choice would make for a boring class), or to accept that most of what is taught will be forgotten quickly and just assume that the students will need a refresher for old material being reintroduced. Even if students will forget what they are taught, the next time they see it they will remember it faster than when they learned it for the first time.

In order to satisfy the first assertion, making students independent of our teachers, it is not important whether or not students can retain material from year to year. The important part is the process- that way students will be able to come up with answers independently of their teachers. This class is so specific that the retention of the material is not as important as the processes taken to come up with the answers.--Swise 12:58, 17 September 2010 (CDT)

In order to understand this statement, one must first understand the definition of "teaching" and the role of a teacher. The teacher in question is much more than a source of knowledge, the teacher is a pathway, a means to an end, of bringing about knowledge in a student. This is much different than wantonly espousing facts and trivia: the teacher is trying to bring about independent thought and knowledge within a student, not make sure the student memorizes meaningless facts and methods. Teaching, in this since, is closely related to the Socratic Method: every student inherently knows the information; it is the instructor's job to show to the students that they themselves know it.

Thus if the goal of teaching is to make the student independent then it is logical to assume that it matters not if the student retains the memory so much as he/she knows innately how to reduplicate the information. Scholarly independence, in other words, is not the ability for the student to retain specific details or material but to have such an intimate knowledge of the subject of interest to intrinsically know the nature of the information: to know what it means, how to derive/use such information, and the implications of it. If a student can do these things, then he/she is truly independent of his/her teacher.--Zlong 23:00, 17 September 2010 (CDT)

Even though some people will forget the basic concepts taught in math classes, I don't think it matters very much. Everyone who retains the information have a reason to; they will most likely either go into higher levels of math that build on this prior knowledge or they will actually apply the mathematical concepts in their later life, career, etc. The people who forget the information probably just don't care because they will never use this math ever again. This math may not be helpful to their later lives so they have little motivation to retain the information. --Amai 13:00, 17 September 2010 (CDT)

I agree with both points. In my own personal experience, the best way to address the second concern is to learn one concept from multiple angles, whether it be a second form of the same explanation perhaps worded differently or a second explanation altogether. That way, if you forget one of the explanations for a concept, you'll maybe remember the other ones; moreover, each time you read another explanation of something, you're reinforcing that something into your brain in multiple areas. However, even this will not make a student "independent" because he or she is still relying on others' explanations. Perhaps the best solution to the retention problem is to focus more on the reasoning of the proofs and making them so easy to understand and obvious that students can come up with them on our own. --Dzhang 13:01, 17 September 2010 (CDT)

It is often unnecessary to retain much of the information learned in school, because much of it is too specific and detailed to be relevant in life. What is important is learning how to think in order to reach a solution, which can be learned through gaining specific knowledge at school, but is not lost when the specific knowledge is lost. Therefore, the lack of retention of information should not be a major concern in making children independent of their parents and teachers. However, if your priority in making children independent is information retention, repetition is probably the best way to increase the percentage of information that is retained. --Kzhu 13:24, 17 September 2010 (CDT)

If the goal of teachers is to make students independent, then just the mastery of a concept can be seen as an indication of success. Being able to learn independently is more important than retaining the actual course material learned. The information learned may be relevant to only one field of study, while the ability to learn independently can be applied to all subjects. Even if a specific concept is forgotten, students should be able to re-learn it on their own. --Awang 13:36, 17 September 2010 (CDT)

Although it is important for students to retain information, retention is not the key to independence. The information learned in previous classes paves the way to independent thinking, but ultimately, it is more important that the students are able to think through a problem and then solve it, rather than memorizing ways to solve it. However, it is important that they learn key concepts in their classes in order to be able to think through the problem, so the basics should probably be repeated each year in order for students to retain them.--Sheinle 13:45, 17 September 2010 (CDT)

It is true that many students have difficulty retaining information which they learned in a course the year before. However, this is not very important unless the student is planning to go into a career which is relevant to that course. It is more important that the student learns how to approach problems independently rather than memorizing facts and formulas.--Yarefeen 13:50, 17 September 2010 (CDT)

If only the concepts of a certain subject are taught in school, then the educators have not done their job properly. The job of teachers is not to tell the students what to do when they are given a problem, but also to help the students learn to think independently and figure out how to do the problem on their own. After a year is over students may not be able to retain all of the concepts taught throughout the year but they should be able to approach a problem from many different angles and figure it out by themselves, despite whether or not they know the exact method most commonly used for the problem. As students work problems a year after they learned the information, they should be able to remember some of the forgotten information that they were taught. --Mhansen 13:51, 17 September 2010 (CDT)

Although students usually forget whatever they learn in a course within the next year, their forgetfulness does not have lasting implications. Unless they forget how to do basic math or read, they will probably turn out fine later on in life. It won't matter what the date of the Battle of Bunker Hill is or what the Animal Phyla are. However, what students do learn in school is how to learn. They learn problem-solving skills that will serve them later in life. Using these skills, students will (hopefully) no longer be reliant on a teacher to explain a concept to them; they will be able to reason through it themselves. --

Although retention may not be exact, students use the foundations from what they do retain in previous classes to excel in classes currently taking. The specifics details from a history course may go forgotten, but when a student develops their argumentative writing skills, it sticks with them. In math, one thing I've definitely learned from taking the honors math classes is how to apply what I've learned in class to learn something new independently. Independent learning is key to success and helps students develop. --Alandrum 14:24, 17 September 2010 (CDT)

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Although some teachers emphasize the importance of retaining information such as definitions and formulas,most students fail to retain so much information after a year-long course. Being able to memorize such things is not important; what matters is the ability to understand the concepts taught in class and being able to apply them in different situations. Thoroughly understanding math concepts allows students to figure out problems even though they may not have all the formulas memorized. --Areyes 14:27, 17 September 2010 (CDT)

The things we learn in school are very important and make us sound smart when we talk to people. --Kwong 14:28, 17 September 2010 (CDT)

Although teachers attempt to teach students what they need to know in order to become independent, students usually look at classes with the wrong outlook. They only see the class as a way to get either a good or a bad grade that can help them get into a good college or into a good job, rather than a way to absorb information that could potentially be useful in the future. They do not learn the real use of education until they are older and realize that instead of having to relearn what they learned in Middle School and High School, they could have learned the information taught to them for the sake of learning. --Mmucasey 14:39, 17 September 2010 (CDT)

Teachers provide information. We, the students, decide whether or not we want to learn the information. If we do learn the information, it may be something that we dislike immensely which could lead to unhappiness or depression during the learning process. If we don't learn the information, we may face the consequence of receiving a bad grade which would cause us to fail high school. Then your parents will kick you out of their house and you will have to work at a local burger king so you won't starve to death. Then one day, you will accidentally spill some fries and you will knock over a bunch of napkins onto a nearby stove. The napkins will catch on fire and burn down the entire burger king which will get you fired immediately. The manager will demand you to pay for the burger king so you will spend all your life savings (which you have been saving up since you got kicked out of your house) to pay for the burnt down burger king. You will then be reduced to homelessness and you will scavenge the streets for bits of food. You will sleep under highway 59 and you will become addicted to drugs. Then one night you run out of money for more drugs and when you are lying in a ditch muttering about nothing at all, you will look back and think "Gee, I wish I learned how to do derivatives in high school." --Syu 14:40, 17 September 2010 (CDT)

The goal of students is to appreciate graciously the efforts of our teachers to instill in us a sense of preparedness and self-confidence, not only to tackle difficult quandaries academically, but also in life in general. Though it is true students ultimately retain very little of the details of each class, I've found that I've taken away much more useful skills from my classes than being able to name the molecular structure of every polyatomic ion known to man, which I will (hopefully) never need again after passing Chemistry sophomore year. Classes that toss you into straight deep waters not only force you to learn, but also force you to learn how to learn. After all, it wouldn't be a DLR class without a little bit of drowning, right? But no one's died yet, and apparently all we have to do in life is die, so I'd say we're faring pretty well. --Myuan 21:20, 17 September 2010 (CDT)

I would just like to point out that if the material is "successfully mastered," then we wouldn't have this retention problem, would we? I believe that if one has truly "mastered" something, he/she has the capability to recall that information. Maybe some enlightenment is needed to remind us of the thoughts, but we should still be able to dig out what we have learned. While I do agree with the idealistic statement stated above, (seeing as it isn't possible for us to ask for help on every little issue we have) we do have to consider that when we're learning something that we have no prior knowledge of, asking questions is probably the most efficient method for clearing the confusion in our minds. Even though qualities such as self-reliability and confidence are important attributes that we need for our lives ahead of us, learning something new requires some guidance so that we know we're headed in the right direction. In other words, we can't learn to fly by ourselves if we don't even know how to flap our wings. --Patrick Wu----Pwu 22:14, 17 September 2010 (CDT)

I guess this has been said a lot already, but I think that retention isn't as important as long as students understand the process of coming up with the answers to their problems (independently or with limited guidance). Students really only need to retain fully the information that goes with them into their profession (for example, I have no intention of becoming a US history teacher or scholar, so memorizing dates for every event in US history is not as important for me as are different math and science concepts). If we had to retain every bit of material we learned from the previous year, our heads would probably explode, plus we're wasting brain space we could be saving for information that is actually important to our specific specialties. It's much more important that students know how to find independently the information they didn't retain to solve problems that they encounter later on. They're using the independence they learned in high school to help them solve the whole "I failed to retain everything" problem. We should teach kids how to learn (if it's independently, then even better), not just stuff them with tons of facts that they won't remember a year later. --Jjuzswik 14:21, 18 September 2010 (CDT)

If the goal of teachers is to make their students independent of them, than it would stand to reason that its inverse, that students aspire to outgrow dependence on their teachers, is also true. We strive to develop the skills necessary to function successfully in the outside world, and it's the task of our teachers to help equip us with these tools. I guess it's valid to say that attempting to ensure retention of course material over extended periods of time is essentially an exercise in futility. Faced with complicated material spanning several subjects, we as students will often resort to less-than-ideal means of studying and displaying proficiency in our courses, meaning that while we don't necessarily regurgitate information, we don't always strive to commit it to long-term memory, either.

Changing this process would require a fundamental restructuring of our education system as a whole, including forcing specialization and the selection of a specific academic field upon students at an age much earlier than their sophomore year of college, and would therefore be both infeasible and inadvisable. Thus, for teachers working to achieve their goal under the restriction of the research you mentioned, the matter of importance should be the degree of independence that they have inculcated in their students.

While we're not entirely focused on perfecting our understanding of every single course we're studying, opting for quantity (comprehension in a wide array of subjects) instead of quality (expertise in a single one), because the goal of our teachers, as stated above, is not always that we master their class material, this flawed system of learning is actually a non-issue. Thus, we can somehow reach a mutually satisfactory, albeit paradoxical, arrangement in which we're not remembering exactly what you're teaching us, but that both teachers and students are happy with because it's more beneficial for us in the long-term.

So the ideal course, in this case one that achieves the goals of both the student and teacher, then becomes not one that forces memory of subject-matter, but instead emphasizes that learning process as well as the practice of solving problems without outside assistance. Teachers should strive to make their students independent of them in life in general, not solely in their area of expertise, by instilling in them a sense of autonomy as well as the capability to face and overcome the obstacles they will come across without dependence on others. By doing so teachers provide their students with the capabilities needed to thrive throughout life, instead of driving them to achieve fleeting success in one field. --Bkumar 18:11, 18 September 2010 (CDT)

Independence should not be the final goal of teachers, it may be a result of achieving other goals, but alone this objective would lead to failure. If independence were the only aim, there would be no point in attending school, for truthfully much of what we learn is pointless in the pursuit of independence. In terms of math, how often to regular people need to derive a theoretical function unless they are engineers or professional mathematicians. The point is that we don't need to learn everything we do at school to reach independence, we learn it because we want to and outside subjects can help clarify whatever field we decide to enter. Almost every student could leave school and be independent at the age of thirteen, but most people stay in school so that they can feel well-rounded later (and get a job better than at McDonald's). In terms of retention, for most that isn't really the point, really all people want to know is that at some point in their lives they knew World History or Calculus, and when they enter their employment, whatever they needed to know will be retained and the rest will be forgotten, but the experience will still remain. --Gbailey 19:23, 18 September 2010 (CDT)

According to this statement, a well-taught student should be able to take the foundation of what was taught and apply as well as develop it in the context of a more complex problem without the assistance of an instructor. I agree with Bhagwat in that a good teacher would also give to his student confidence and autonomy in solving problems in general, not only within the specific subject being taught. As Bhagwat stated, a perfect teacher would also give the student "the capabilities needed to thrive throughout life." However, a single teacher may have upwards of a hundred students, and to provide these skills the teacher must have a close connection to each individual under his/her tutelage - a connection that is not possible when there are numerous students to be taught. If this is the case, it is a momentous achievement in itself for the teacher to communicate skills as universal as how to approach a situation in general. --Pbhamidipati 19:36, 18 September 2010 (CDT)

The fact that course material is not as "successfully mastered" as we would like to believe, while not surprising, is also not as detrimental to the learning process as one would first conclude. One of the key elements of learning, as previously stated, is developing the ability to independently reason and problem solve. Although this is not the only thing we as students gain from the learning process, it ultimately is one of the most essential in preparing us in terms of self-confidence and the ability to function independently. While classes focusing on memorization and concrete facts are certainly less strenuous and therefore somewhat more enjoyable from a student perspective, it is ultimately the classes that challenge our ability to think and fend for ourselves that have a lasting impact on us as individuals. --Clee 20:55, 18 September 2010 (CDT)

Although we aren't capable of retaining everything we learn, it is much easier to re-learn something than it is to learn it the first time. After a quick review, we should be able to recall everything we had "succesfully mastered." Because of this, teachers should not assume that their students will remember how to integrate, what a noun is, or any other facts they learned the year before. I think There should be a quick review before continuing.

Even though we cannot recall the information, it is still important to teach it so we can re-learn it and so we can develop the skills necessary to learn new skills and concepts. Teachers should teach their students could habits for doing work and getting stuff done.--Wrogers 11:56, 19 September 2010 (CDT)

Even though it is true that many students do not retain important information that they have learned in years past, this retention should not be an enormous factor fulfilling the teacher's goal of making us independent of him. Teachers reach this goal by successfully ingraining in students the process of how to solve certain problems, instead of just making them memorize certain formulas and information. Teachers are successful if they can teach students HOW to learn, not just WHAT to learn in their particular class. That way the teachers would make the students independent of them, because those students could use the process of how to learn and translate it to the rest of their lives and other classes. Also, information that is not retained could quickly be relearned the next year if necessary. Therefore, despite your concerning "other information," the ideal statement still holds true because retention and independence are not necessarily intertwined. --Mlewis 14:51, 19 September 2010 (CDT)

The lack of retention of important information that seems to plague students is a natural part of the learning process. There is no conceivable way to remember everything we learn indefinitely. So what we can do about this problem is to learn to deal with it. Teachers who are unhappy with this will review past concepts to strengthen their student's foundations in learning. Students who are bothered by this will continually review information so they won't forget. This problem with retention is just another natural obstacle in life that we all need to learn to overcome. --Jpham 16:34, 19 September 2010 (CDT)

It takes time to retain information, but I think that SJS students have so much going on that there is limited time to properly study. We end up cramming and then forgetting because there's no time for repetition. I think the problem is that we often don't see how certain concepts apply to real life, so we don't find it necessary to put in the time to really retain it. As in, the goal becomes learning it for the test rather than learning long term. I think if we spent longer on each lab and did more problems then we'd remember the concepts better. However, the point of an honors course is for each student to manage their time and learn accordingly. I know some people wouldn't be too pleased if we decided to slow things down. --Stan 17:04, 19 September 2010 (CDT)

A teacher's primary goal should be somewhere in between encouraging students' total independence and complete dependence. If the teacher only encourages the former, then he or she is not really teaching but just strongly encouraging their students to figure stuff out on their own. Yet if the teacher babies his or her students through all the concepts, then he or she is not really providing them with any self-guided learning skills which will be invaluable to students later in life. Students, like all people, forget things. If the student "successfully mastered" the material and later forgot it, then "remastering" the information later should not be a huge burden. That's what the internet is for. --Gpeterkin 20:24, 19 September 2010 (CDT)

Many high school students might feel like they are forced to take courses that don't interest them and are not directly applicable to their life. The way they process information and their motive for learning is not touched upon by the traditional high school curriculum. Students are expected to learn the class material and figure out on their own the connections between what they are learning and how that material will be used. The hands-off-occasional-prodding method of teaching is beneficial to students who are eager - or at least willing - to explore and look for connections on their own, but without a draconian teacher breathing down their necks, more reluctant students will suffer. In the end, the effort put forth by the student will determine the effect of the teaching. The teacher cannot overcome a student's unwillingness to learn. Question is: how do teachers get students to make connections between what they are learning and what they have experienced? (How do teachers get students to care?) -vchu

If teachers hope to improve retention of information, the best method would be to give both some practical application that makes the material seem important and the most basic understanding of what the information is founded on. Without understanding the basis of a topic, students will see it as some other useless tidbit, and when lost has nothing on which to be relearned. With a basis for the information, even if it is lost, the fundamental concept on which it is founded will remain, making relearning easy and possible even during a test (I have recreated formulas from scratch during tests). The practical application of information encourages students to think more about it, and understand how it really works, instead of some vague concept of which value goes where in the formula. Without understanding the practical application, the information is essentially useless and can be quickly forgotten.--Jnaruk 12:08, 21 September 2010 (CDT)